Manager angry I am not flexible with my shifts

[Jobstress1]

I started my job a year ago. It is in a small business with the owner and 10 employees. I replied to the advert which requested flexible working including Sundays, I said I could do 3 days (including every Sunday) every Tuesday and every Friday. The owner who interviewed me said that was fine but that she wanted flexible cover when people were on holidays. I said I would try cover where possible but I have a 1.5 year old so am stuck to these hours unless my DH is on annual leave.
All fine, I got the job. I work hard, they are happy with my work (afaik) never rung in sick or anything. The problem is everytime anyone is on holiday I get in trouble for not being flexible. My DH and my best friend have taken annual leave to help me so I can cover more days, but obviously this isn't everytime everyone is on holiday.
I am feeling really upset over this. The owner is talking behind my back saying I need to work more shifts but I am physically unable to do so.
I realise the owner said up front he needed flexible cover over holidays but I also was honest from the start and stated what hours I could definitely do.
I don't know what to do. Should I leave? I have had a lot of stress at home and have never let that impact on my job. I am a good employee but am made to feel like I am being awkward refusing to cover- I would if I could.
Just to add, when my DH happened to have a week holiday the same week one of my colleagues was off, I worked 6 days that week. I will always do it if I can.
I don't know what to do, it is getting me down.

I'd start looking for another job; you were honest when you told them what hours you could do, so the owner can't really complain that you can't do more than that.

Look for another job but don't let them hound you out of this one - you were upfront and they hired you anyway. It's not your problem to fix.

I agree that it’s time to look for another job.

To be honest they did say they needed flexibility. They were upfront and it implies you said you would try to be flexible. Either look for a job with fixed hours or find childminders/babysitters who can be flexible

I’d think they’d find it difficult to find anyone who can work what they want, I’d think most people either work part time because they’ve got caring responsibilities or are doing other things on the days they don’t work or they’d be working full time.

Trying to be flexible is not the same as guaranteeing you will be. OP has been as accommodating as she can be, but workers do have lives that can't be completely within the employer's control.
I agree with pp that they will find it hard to get a part time worker who is completely available when it suits them